DagSemProc.06201.11.pdf
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Vertex reconstruction in Cayley graphs
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Dagstuhl Seminar Proceedings, Volume 6201
Series: Dagstuhl Seminar Proceedings (DagSemProc) - License:
Creative Commons Attribution 4.0 International license
- Publication Date: 2006-11-07
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Elena Konstantinova. Vertex reconstruction in Cayley graphs. In Combinatorial and Algorithmic Foundations of Pattern and Association Discovery. Dagstuhl Seminar Proceedings, Volume 6201, pp. 1-20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2006)
https://doi.org/10.4230/DagSemProc.06201.11
https://doi.org/10.4230/DagSemProc.06201.11
Abstract
In this report paper we collect recent results on the vertex
reconstruction in Cayley graphs $Cay(G,S)$. The problem is stated as
the problem of reconstructing a vertex from the minimum number of
its $r$-neighbors that are vertices at distance at most $r$ from the
unknown vertex. The combinatorial properties of Cayley graphs on the
symmetric group $Sn$ and the signed permutation group $Bn$ with
respect to this problem are presented. The sets of generators of $S$
are specified by applications in coding theory, computer science,
molecular biology and physics.
Keywords
- Reconstruction problems
- Cayley graphs
- the symmetric group
- the signed permutation group
- sorting by reversals
- pancake problem
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